If you run a test to back up only the System States on those affected servers during the day from a new selection list, does it give you the same error?
If it doesn't, you most likely have a corruption in your selection list/your backup job is not configured correctly.
You can then look at:

1. Deleting the selection list, and recreating from scratch.
2. Checking your backups that run during the week and make sure that the settings there (like AOFO) are the same as the backup job over the weekend that completes successfully.